# „Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes.“

—  Archimedes, buch On the Equilibrium of Planes

Book 1, Propositions 6 & 7, The Law of the Lever.
On the Equilibrium of Planes

Letzte Aktualisierung 22. Mai 2020. Geschichte
##### Archimedes4
antiker griechischer Mathematiker, Physiker und Ingenieur -287 - -212 v.Chr

## Ähnliche Zitate

### „The Pythagoreans discovered the existence of incommensurable lines, or of irrationals. This was, doubtless, first discovered with reference to the diagonal of a square which is incommensurable with the side, being in the ratio to it of &radic;2 to 1. The Pythagorean proof of this particular case survives in Aristotle and in a proposition interpolated in Euclid's Book X.; it is by a reductio ad absurdum proving that, if the diagonal is commensurable with the side, the same number must be both odd and even. This discovery of the incommensurable… showed that the theory of proportion invented by Pythagoras was not of universal application and therefore that propositions proved by means of it were not really established…. The fatal flaw thus revealed in the body of geometry was not removed till Eudoxus discovered the great theory of proportion (expounded in Euclid's Book V.), which is applicable to incommensurable as well as to commensurable magnitudes.“

—  Thomas Little Heath British civil servant and academic 1861 - 1940

p, 125
Achimedes (1920)

### „Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison with regard to quantity is accomplished in the case of discrete magnitudes by counting, in the case of continuous magnitudes by measuring. Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case also we can only determine the more or less and not the how much. The researches which can in this case be instituted about them form a general division of the science of magnitude in which magnitudes are regarded not as existing independently of position and not as expressible in terms of a unit, but as regions in a manifoldness.“

—  Bernhard Riemann German mathematician 1826 - 1866

On the Hypotheses which lie at the Bases of Geometry (1873)

### „Slavery is an evil of Colossal Magnitude.“

—  John Adams 2nd President of the United States 1735 - 1826

Letter http://founders.archives.gov/documents/Adams/99-02-02-7261 to William Tudor, Jr., 20 November 1819. Partially quoted in Founding Brothers : The Revolutionary Generation (2000) by Joseph J. Ellis, p. 240
1810s
Kontext: I Shall not pause to consider whether my Opinion will be popular or unpopular with the Slave Holders, or Slave Traders, in the Northern the Middle, the Southern, or the Western, States—I respect all those who are necessarily subjected to this Evil.—But Negro Slavery is an evil of Colossal Magnitude. … I am therefore utterly averse to the admission of Slavery into the Missouri Territory, and heartily wish that every Constitutional measure may be adopted for the preservation of it.

### „Thou liar of the first magnitude.“

—  William Congreve, Love for Love

Act II, scene ii
Love for Love (1695)
Variante: Ferdinand Mendez Pinto was but a type of thee, thou liar of the first magnitude.

### „Look at the magnitude of this subject!“

—  Abraham Lincoln 16th President of the United States 1809 - 1865

1860s, Allow the humblest man an equal chance (1860)
Kontext: Look at the magnitude of this subject! One sixth of our population, in round numbers — not quite one sixth, and yet more than a seventh, — about one sixth of the whole population of the United States are slaves! The owners of these slaves consider them property. The effect upon the minds of the owners is that of property, and nothing else — it induces them to insist upon all that will favorably affect its value as property, to demand laws and institutions and a public policy that shall increase and secure its value, and make it durable, lasting and universal. The effect on the minds of the owners is to persuade them that there is no wrong in it. The slaveholder does not like to be considered a mean fellow, for holding that species of property, and hence he has to struggle within himself and sets about arguing himself into the belief that Slavery is right. The property influences his mind. [... ] Certain it is, that this two thousand million of dollars, invested in this species of property, all so concentrated that the mind can grasp it at once — this immense pecuniary interest, has its influence upon their minds.

### „It is evident that we cannot mean to affirm that the stars of the fifth, sixth, and seventh magnitudes are really smaller than those of the first, second, or third, and that we must ascribe the cause of the difference in the apparent magnitudes of the stars to a difference in their relative distances from us.“

—  William Herschel German-born British astronomer, technical expert, and composer 1738 - 1822

Ch.4 "Life and Works" from a memoir, published (1817).
Kontext: It is evident that we cannot mean to affirm that the stars of the fifth, sixth, and seventh magnitudes are really smaller than those of the first, second, or third, and that we must ascribe the cause of the difference in the apparent magnitudes of the stars to a difference in their relative distances from us. On account of the great number of stars in each class, we must also allow that the stars of each succeeding magnitude, beginning with the first, are, one with another, further from us than those of the magnitude immediately preceding.

### „This is not a Budget, but a revolution; a social and political revolution of the first magnitude.“

—  Archibald Primrose, 5th Earl of Rosebery British politician 1847 - 1929

Letter to the The Times attacking the "People's Budget" (22 June 1909), p. 8.

### „Every magnitude, every dimension, requires a new configuration.“

—  Fritz Wotruba Austrian sculptor (23 April 1907, Vienna – 28 August 1975, Vienna) 1907 - 1975

Quelle: The Human Form: Sculpture, Prints, and Drawings, 1977, p. 10.

### „But simply through magnitude a body does not receive motion“

—  Robert Grosseteste English bishop and philosopher 1175 - 1253

De Luce seu de Inchoatione Formarum (c. 1215-1220)
Kontext: One cause, in so far as it is one, is productive of only one effect. I do not rule out several efficient causes of which one is nearer and another more remote in the same order. Thus when I say simply 'animal', I do not exclude another substance or particular substance. Hence motion, in so far as it is one, is productive of only one effect. But motion is present in every body from an intrinsic principle which is called natural. Therefore an efficient cause simply proportional to the motion is present in all bodies. But nothing is present in common in every body except primitive matter and primitive form and magnitude, which necessarily follows from these two, and whatever is entailed by magnitude as such, as position and shape. But simply through magnitude a body does not receive motion, as is clear enough when Aristotle shows that everything that moves is divisible, not, therefore, simply because of magnitude or something entailed by magnitude is a body productive of motion. Nor is primitive matter productive of motion, because it is itself passive. It is therefore necessary that motion follow simply from the primitive form as from an efficient cause.

### „Since, however, all multitude and magnitude are by their own nature of necessity infinite“

—  Nicomachus Ancient Greek mathematician 60 - 120

Kontext: Things... are some of them continuous... which are properly and peculiarly called 'magnitudes'; others are discontinuous, in a side-by-side arrangement, and, as it were, in heaps, which are called 'multitudes,' a flock, for instance, a people, a heap, a chorus, and the like.
Wisdom, then, must be considered to be the knowledge of these two forms. Since, however, all multitude and magnitude are by their own nature of necessity infinite—for multitude starts from a definite root and never ceases increasing; and magnitude, when division beginning with a limited whole is carried on, cannot bring the dividing process to an end... and since sciences are always sciences of limited things, and never of infinites, it is accordingly evident that a science dealing with magnitude... or with multitude... could never be formulated.... A science, however, would arise to deal with something separated from each of them, with quantity, set off from multitude, and size, set off from magnitude.<!--pp.183-184

### „I doubt you can understand the magnitude of the stupidity in your statement“

—  Robert Jordan, The Wheel of Time

Quelle: The Gathering Storm

### „Balanced reciprocity is as much a social compact as it is an economic advantage.“

—  Peter Farb American academic and writer 1929 - 1980

Man's Rise to Civilization (1968)
Kontext: Balanced reciprocity is as much a social compact as it is an economic advantage. It is particularly important in hunting-gathering societies, where no individual could possibly accumulate a surplus, live independently of other members of the band, or become so successful in the quest for food as never to need meat from someone else's kill.<!-- p. 44

### „Another indication of the magnitude of the present transition is the fact that, as far as many statistical series related to activities of mankind are concerned, the date that divides human history into two equal parts is well within living memory.“

—  Kenneth E. Boulding British-American economist 1910 - 1993

Quelle: 1960s, The meaning of the twentieth century: the great transition, 1964, p. 7

### „I think as a kid I never really understood the magnitude of a hurricane and what it could do.“

—  Marshall Faulk All-American college football player, professional football player, running back, Pro Football Hall of Fame member 1973

St. Louis Post Dispatch 2005-08-31.

### „We are lucky that a crisis of this magnitude only comes around once every 80 years.“

—  José Luis Rodríguez Zapatero Former Prime Minister of Spain 1960

In an interview with Spanish national television.
As President, 2008
Quelle: Zapatero evita respaldar a De la Vega y asume que habrá crisis de Gobierno http://www.elconfidencial.com/espana/zapatero-de-la-vega-crisis-gobierno-tve-20100309.html

### „We are each other's harvest; we are each other's business; we are each other's magnitude and bond.“

—  Gwendolyn Brooks American writer 1917 - 2000

Paul Robeson
Kontext: That time
we all heard it,
cool and clear,
cutting across the hot grit of the day.
The major Voice.
forgoing Rolling River,
forgoing tearful tale of bale and barge
and other symptoms of an old despond.
Warning, in music-words
devout and large,
that we are each other's
harvest:
we are each other's
we are each other's
magnitude and bond.

### „As we grow in our understanding of knowledge of Him in heaven, our worship will surely increase in magnitude.“

—  Paul P. Enns American theologian 1937

Quelle: Heaven Revealed (Moody, 2011), p. 180

### „Government is either organized benevolence or organized madness; its peculiar magnitude permits no shading.“

—  John Updike American novelist, poet, short story writer, art critic, and literary critic 1932 - 2009

Act I
Buchanan Dying (1974)

### „Freebooter, n. A conqueror in a small way of business, whose annexations lack of the sanctifying merit of magnitude.“

—  Ambrose Bierce, buch Des Teufels Wörterbuch

The Devil's Dictionary (1911)

### „The way in which the irrational numbers are usually introduced is based directly upon the conception of extensive magnitudes—which itself is nowhere carefully defined—and explains number as the result of measuring such a magnitude by another of the same kind. Instead of this I demand that arithmetic shall be developed out of itself.“

—  Richard Dedekind German mathematician 1831 - 1916

Footnote: The apparent advantage of the generality of this definition of number disappears as soon as we consider complex numbers. According to my view, on the other hand, the notion of the ratio between two numbers of the same kind can be clearly developed only after the introduction of irrational numbers.
Stetigkeit und irrationale Zahlen (1872)